An event F is said to carry negative information about an event F, and we write F E, if P(E|F) < P(E) Prove or give counterexample to the following assertions: a. If F E, then E F.

Q: Let X - Geom(p). Let s 2 0 be an integer. Show that P(X > s) = (1 – p)s. (Hint: The probability that…

A: Geometric distribution In series of Bernoulli trials, the random variable X denotes number of trials…

Q: Prob-3 Pressurized air are being used in a manufacturing company in its daily operation. There are…

A: The events A and B are given as- A : Reciprocal compressor (R) is always off. B: At least one of the…

Q: Given a p.m.f. f(x) of a d.r.v. x as follow: x = 3,4, f(x) = k - , then (0 0. W the value of k to…

A:

Q: IX,- M |1+IX,-X Show that E →0 if and only if X X in probability.

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Q: a. Let A and B be two events such that P(A) = 0.05 and P(A U B) = 0,49. Calculate P(B') if events A…

A: Continue with Simple probability theory...............

Q: 4. Show that an event A is independent of itself iff P(A) is either 0 or 1.

A: Proof: PA=PA∩A=PAPA  Since A is independent itself.⇒PA1-PA=0PA=1  Since P(A)&gt;0

Q: Let S = {a, b, c, d, e, f} with P(a) = 0.16, P(b) = 0.14, P(c) = 0.15, P(d) = 0.25, P(e) = 0.18, and…

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Q: Is Statement (1) below True or False and WHY? TEA=B is equivalent to "TEA IFF TE B"

A: Let us provide justification and check whether both equations are equivalent or not

Q: Show that for any events E and F, P(E|E U F) 2 P(E|F). Hint: Compute P(E|E n F) by conditioning on…

A:

Q: events x and y are such that px = 0.35 and px ∪ y = 0.80. given that x and y are independent and…

A: Given That, p(x)=0.35 p(x ∪ y )=0.80 Given that x and y are independent and non-mutually exclusive…

Q: assume that Pr[A∪B]=0.6 and Pr[A]=0.2 (1) What is Pr[B] if A and B are independent events?

A: Since A and B are independent event, so pr(A∩B)= pr(A)pr(B).

Q: . Write (12)(13)(14) in the form æ(12), where a E A¸. Write (1234) (12)(23), in the form a(1234),…

A: Given, (12)(13)(14) and we have to write this in the form alpha(12), where a in A4. Similarly, write…

Q: Reject Ho if |z| > N

A: We know that  Null hypothesis H0. Alternative hypothesis H1.

Q: If P(An B) = 0.3 find P(A U B°) O 1 0.3 0.7

A:

Q: 6. The prosecutor's fallacy. Let G be the event that some accused person is guilty, and 7 the event…

A: We have to show that the P(G|T)=P(T|G) iff P(G)=P(T)

Q: For any three events A, B, & D. Such that Pr(D)>0. Prove that Pr(A U B|D) = Pr(A|D) ÷ Pr(B|D) - Pr(A…

A: Given that, there are three events A, B &amp; D. We have to prove that, Pr(A U B|D) = Pr(A|D) ÷…

Q: If P(A/B) = P(A) and P(B/A)=P(B), then A and B are: O A. Mutually exclusive O B. Dependent O C.…

A: Equally likely events:   The two events are said to be Equally likely event if every event has the…

Q: Example: Let x=1,2,3,4,5 15 P(x) = show that p(x) is p.d.f elsewhere

A:

Q: If P (A) = 0.3, P(B) =0.6, and P (Aor B) =0.7 are A and B mutually exclusive?

A: Two events are said to be mutually exclusive when both can not occur simultaneously.  A and B are…

Q: a- What is the probability that a soft drink is chosen randomly by a customer? b- What is the…

A: Given Data : Total Number of customers = 80 Number of customers choosing Soft Drink = 18…

Q: Suppose we randomly draw two integers from the range [1, n] with uniform probability. Define X to be…

A: E(|X-Y|) fx|y=1n2 E(Z) = ∑x=1n∑y=1nx-yn=∑x=1n ∑y=1n x-yn2+∑…

Q: Let A and B be events such that​ Pr[A] =0.370.37​, Pr[B] =0.630.63​, and​  Pr[A ∩​ B] =0.240.24.…

A: Required to calculate the conditional probability that A occurs given B has occured, P(A|B)

Q: Let S = {a, b, c, d, e, f} with P(a) = 0.14, P(b) = 0.24, P(c) = 0.21, P(d) = 0.15, P(e) = 0.13, and…

A: From given we have : S = {a, b, c, d, e, f} P(a) = 0.14 P(b) = 0.24 P(c) = 0.21 P(d) = 0.15 P(e) =…

Q: Assume that a sample is used to estimate a population mean,.. Find the 90% confidence interval for a…

A: The population mean is .

Q: 2. Ifj || k a. mZ2%3D b. mZ3 = 47° 1 119° %3D k %D C. m/1 = 3.

A: j || k

Q: (a) Show that if n € N, then <¹dr. n+1

A:

Q: A = [{ -5 11 41 B = 3 -1 li -2 -2. 2 -1 31 Watter van die volgende bewerkings is NIE gedefinieer…

A: Given, order of matrix A = 2 * 3 order of matrix B = 3*2  order of matrix C = 2 * 3 Now we have to…